Calculate $$ \iint \sin(xy^{2}) dA $$ above the annulus $1 \le x^2 + y^2 \le 4 $
Without Polar Coordinates.
Attempt :
Since the region is symmetric, I can also calculate for just $1/4$ of it first. But notice that in the end I have to calculate
$$ \int \frac{ \cos(y^{2} \sqrt{4-y^{2}}) }{y^{2}} dy $$
If I change the order of integration I have to calculate
$$ \int \sin(xy^{2}) dy $$
How to solve this? Thanks.